Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x-2y &= 2 \\ 3x+4y &= -4\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $3x = -4y-4$ Divide both sides by $3$ to isolate $x$ $x = {-\dfrac{4}{3}y - \dfrac{4}{3}}$ Substitute this expression for $x$ in the first equation. $2({-\dfrac{4}{3}y - \dfrac{4}{3}}) - 2y = 2$ $-\dfrac{8}{3}y - \dfrac{8}{3} - 2y = 2$ Simplify by combining terms, then solve for $y$ $-\dfrac{14}{3}y - \dfrac{8}{3} = 2$ $-\dfrac{14}{3}y = \dfrac{14}{3}$ $y = -1$ Substitute $-1$ for $y$ in the top equation. $2x-2( -1) = 2$ $2x+2 = 2$ $2x = 0$ $x = 0$ The solution is $\enspace x = 0, \enspace y = -1$.